As a newbie myself, who has been reading and keeping notes for a couple of months and think I am beginning to understand things, I'll share my notes, as somewhat of a "dummy" guide. This is a basic outline, not from experience (my components are ordered/being shipped), but just my summary of what I think I hear as the majority opinion here. But as others said, things change fast. YMMV, literally.

These notes are mostly about an ebike conversion, as opposed to buying a commercial ebike, but many of the same concepts apply.

In an ebike conversion, the major components are the bike, motor, controller, batteries, and the rider's needs/wants. The last one is the most important, but a little technical detail is needed to make sense of that, so the others first:

1. The Bike

Anything goes, really, but steel or cromoly is generally preferred, especially for the dropouts, especially for a front motor. Use a magnet to assess; it will stick to steel or cromoly, but not to Aluminum, carbon, etc. No suspension on the front forks if using a front motor.

The bike needs storage for the batteries. A rack on the back is probably the most common choice; batteries in the frame triangle require a custom box/bag (no good solution there yet really).

Those on the forum doing high speeds (above about 25 mph, especially >30 mph) are often looking for a suitable full-suspension bike, because bumps are harsher and more dangerous at higher speeds. Unfortunately, there are few full-suspension bikes with lots of space in the triangle. There are a couple of threads where some possibilities are discussed ( Suitable full suspension frames and Bike frames suitable for frame mounted batteries and speed)

2. Motor

A brushless hub motor is the main choice. Other types (through separate chain, friction drive etc) are not for dummies, but if cheaper is key then you could look into them.

In brushless hub motors, the two types are geared or direct drive (DD).

Geared hub motors have a fixed internal gear ratio which allows the motor to operate at a more efficient higher motor speed for a given wheel speed. Geared motors are lighter, and have better torque at low speed, but no regeneration is possible. They are not as good for very high power, typically, as the gears can be damaged. Makes a slight whining noise. They freewheel, that is, they give no drag when pedalling without power to the motor.

Direct drive (DD) hub motors are simpler, quieter, often cheaper, and can "scale" to higher voltage/power without risk of damage. They can be used with regenerative braking, which is good for braking, but not so great at extending battery range (~ 5%ish).

A hub motor can go on the front wheel or on the back. The front is a little simpler, but the back is safer, especially for high power. A torque arm (or two) is a good addition for helping ensure that the axle does not spin out (recommended on the front wheel for sure, preferred even on the back, especially if using high power).

Not all motors can take disk brakes. Those that do have limited clearance so not all disk brakes will fit.

A very useful reference is the hub motor simulator on ebikes.ca (http://ebikes.ca/simulator/). It shows the motor power output, torque, and efficiency as a function of speed for different choices of motor, battery, and controller parameter combinations.

3. Controller

The controller is the brain that receives the throttle control and brake signal (to cut power or use regeneration when braking) and decides what power to pull from the battery and send to the motor.

Controllers are sensored (more common) or sensorless; some can do both. Hall sensors "know" the position of the motor rotation and help the controller know how to power the motor for smooth acceleration.

The infineon type is probably the controller type of choice now on E-S (lots of threads here on how to adapt etc). The ones sold by Lyen are valued among the high speed crowd.

Typical controllers handle at least 36V and 15A. More common here would be to handle up to at least 48V nominal and minimum of 20A, even 25A. Really high power ones will handle up to 72V or more, 35A or more.

the factor 1.25 is to leave 20% unused before recharging, otherwise battery life is reduced. Add another 20% if you plan to keep batteries for a long time, because capacity will decline with battery age.

Charge/discharge rate is expressed in "C", the battery capacity. A rate of 1C is the full battery in one hour. For example, a 10 Ah battery discharged at 10 A would be a 1C discharge, at 20A is 2C discharge (and would last only 0.5 hour).

LiFePo4 or LiPo are the main choices now. Another possibility is to get batteries from old tool packs etc. sold by some members on E-S.

LiFePo4 is more expensive up front, heavier, no fire risk, theoretically longer life (1000s of charges). pingbattery is one of the best values, but they need a lower C of 1-2C average or battery life is considerably shortened compared with other LiFePo4 choices. So ping batteries (or others with similar C rate) need a higher total capacity to keep the C-rate low enough. E.g. with a 25A controller, get at least 15 Ah.

LiPo is (recently) the cheapest, lightest choice, but needs careful charging or is extreme fire risk (read the Golden Rule and buy LP-Guard or similar fire-containing bags). HobbyKing is the popular source for LiPo right now. Newer quality LiPo can handle >>5C discharge and >2C charge rates; the former means you buy only the capacity you need, the latter means quicker recharges are possible. With LiPo you usually will have to buy several packs and parallel them together for higher Ah (e.g. 2x(5 Ah)), then series connect for higher voltage (e.g. 2 "5S" subpacks for 37 V nominal).

Both LiPo and LiFePo4 packs are sold with terms like "6S2P", which refers to the number of individual cells in series (S) and in parallel (P) within the pack. LiPo cells are nominal 3.7 V each; LiFePo4 cells are nominal 3.2 V each.

Batteries need chargers -- LiFePo4 usually comes with a charger. If LiPo, you should buy a good charger. (Experts sometimes bulk charge directly with a power supply, but "dummies" need one made for LiPo). Popular chargers now seem to be the iCharger 208B+ or 1010B+, or others in the iCharger line, or the Hyperion EOS 1420i. But they (like many chargers) require a separate power supply. Have a look at E-S threads for details, there's too much to explain in a quick guide.

Batteries charge to a fair bit higher than their nominal voltage, and voltage declines as they are discharged. They can be damaged if charged too high, or discharged too low, so they need HVC (high-voltage cutoff) and LVC (low-voltage cutoff) protection. Packs are happier if they are "balanced", i.e. all the cells are have very nearly the same voltage, especially if paralleling subpacks together. Some packs come with a BMS (Battery Management System) computer board built-in to control charging/balancing and protect the batteries from high or low voltage (this is typical with LiFePo4 packs). There are also third-party BMS boards that are sold by E-S members. For LiPo, the charge control/balancing is done by the separate charger, and LVC may be provided during use if desired by add-on monitors (e.g. Battery Medic, Chargery BM6, etc).

Many people also monitor their power use through a small computerized device such as the Cycle Analyst ("CA" everywhere on E-S) or the Watts-up meter. The Cycle Analyst can also measure and limit speed and power use, which can assist in meeting legal requirements.

5. The rider

Your needs/wants likely fall roughly into one of the following categories:
(a) assist power (for higher average speed, help climbing hills) in addition to normal biking with you pedalling
(b) basic medium power, legal (N. America) or not much over (pedalling not necessary, decent speed even up hills)
(c) crazy power, high speed

(a) Assist Power
For assist power, your motor should be minimum 350W (up to 500 nominal), geared (freewheels, so no drag when not using power) or DD okay. Front wheel (+torque arm, always) or back okay. Controller and batteries rated for 36V, at least 15-20A.

In some countries, lower powers are needed to be legal, can be as low as 250W, 24V, 10-14A. More commonly, use at least 36V and 20A, which will get approximately 20 mph (32 km/hr) on level ground. Go to 48V and 25A to maintain 32 km/hr on small hills and headwinds, or to get better speeds up steep hills.

(b) Medium Power
For medium power, you likely want a DD hub motor, nominal 500W or more. A geared motor is okay if at the lower power end. Front hub is okay, but the back hub motor is preferred if going to higher power. Controllers and batteries rated for minimum 36V, probably 48V, 25A.

(c) High Power
For really high power, almost certainly use a DD motor, almost certainly on the back, probably a Lyen controller. Voltages >> 48V, currents >= 30A. Don't go straight to (c), start with (a) or (b) unless you really know what you are doing.

Batteries will be $250 to >$500. Example: HobbyKing LiPo, 36V 10Ah, on sale can be ~$200 shipped, but a good charger will be ~$80-$120 and a good power supply for it ~$40-$80. LiFePo4 from Ping, 36V 15Ah is ~$450 shipped, with a 2A charger included. But these numbers are changing fast.

Bottom line is this can only be a guide. Your needs/wants for speed, distance, type of bike, etc. will dictate a lot more details. The group here is great at answering questions.